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The subset sum problem (SSP) is a decision problem in computer science. ... Moreover, some restricted variants of it are NP-complete too, for example: [1]
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
The subset sum problem is a special case of the decision and 0-1 problems where each kind of item, the weight equals the value: =. In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. [2]
(An example of this is the subset ... Sum of sets. The Minkowski sum of two sets and of real numbers is the set + := {+:,} consisting of all ...
It is based on the subset sum problem (a special case of the knapsack problem). [5] The problem is as follows: given a set of integers A {\displaystyle A} and an integer c {\displaystyle c} , find a subset of A {\displaystyle A} which sums to c {\displaystyle c} .
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
Minkowski sum A + B. For example, ... However, the Minkowski sum of two closed subsets will be a closed subset if at least one of these sets is also a compact subset.